1. Areej Jouhar & Hafsa El-Zain 2015-2016 Biostatistics BIOS 101 Foundation year

2. LEC3 * ● Construct and interpret a histogram ● Create and interpret bar charts, pie charts, and stem- and-leaf diagrams ● Present and interpret data in line charts and scatter diagrams Lecture goals 2

3. Data set shows a continuous quantitative variable, serum cholesterol measured on a sample of stroke patients LEC3 3.74.85.45.66.16.47.17.68.4 3.84.95.45.66.16.47.17.68.4 3.84.95.55.76.16.47.17.69.3 4.45.15.55.76.26.47.17.79.5 4.55.15.55.76.36.47.27.810.2 4.55.15.65.86.36.47.37.810.4 4.55.15.65.86.4 7.47.810.6 4.75.25.65.96.4 7.48.210.8 4.75.35.666.47.17.58.310.8 4.85.35.66.16.47.17.58.310.9 Example 3

4. LEC3 * Class FrequencyRelative frequency PercentCumulative percentage 3-513 (13/90)= 0.14 14% 5-745 (45/90)= 0.50 50%64% 7-924 (24/90)= 0.27 27%91% 9-118 (8/90)= 0.09 9%100% n=90 4 Frequency distribution

5. LEC3 *  The Classes or Intervals are shown on the Horizontal Axis  Frequency is measured on the Vertical Axis  Bars of the appropriate heights can be used to represent the number of observations within each class  Such a graph is called a Histogram 5 Histograms

6. No gaps between bars, since continuous data ((Serum cholesterol (mmol/L) measured on a sample of 90 stroke patients )) Serum cholesterol (mmol/L) Frequency LEC3 * 6 Histogram Example

7. ● Frequency Polygon is a special kind of line graph. ● firstly place a dot above the midpoint of each class. ● the height of each class above horizontal axis corresponding to the frequency of the relevant class. 7 The frequency polygon

8. 8 histogram frequency polygon

9. LEC3 *  Number of Data Points Number of Classes under 50 5 - 7 50 – 100 6 - 10 100 – 250 7 - 12 over 250 10 - 20  Class widths can typically be reduced as the number of observations increases  Distributions with numerous observations are more likely to be smooth and have gaps filled since data are plentiful 9 General Guidelines

10. LEC3 *  The class width is the distance between the lowest possible value and the highest possible value for a frequency class  The minimum class width is Largest Value - Smallest Value Number of Classes W = 10 Class Width

11. LEC3 *  A simple way to see distribution details in a data set METHOD: Separate the sorted data series into leading digits (the stem) and the trailing digits (the leaves) 11 Stem and Leaf Diagram

12. LEC3 *  Here, use the 10’s digit for the stem unit: Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 ■ 12 is shown as ■ 27 is shown as ■ 35 is shown as Stem Leaf 1 2 2 7 3 5 12 Example:

13. LEC3 * ● Completed Stem-and-leaf diagram: Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Stem Leaves 12 3 7 21 4 4 6 7 7 30 2 5 7 8 41 3 4 6 53 8 13 Example :

14. LEC3 * 14 Graphing Categorical Data Qualitative (Categorical) Data Pie ChartsBar Charts Pareto Diagram

15. LEC3 *  Bar charts and Pie charts are often used for qualitative (category) data.  Height of bar or size of pie slice shows the frequency or percentage for each category 15 Bar and Pie Charts

16. LEC3 *  A physical therapist wants to get a sense of the types of rehabilitation required by her patients. To do so, she obtains a simple random sample of 30 of her patients and records the body part requiring rehabilitation. See Table blew.  Construct a frequency distribution of location of injury. and use charts too. 16 Bar And Pie Charts Example

17. LEC3 * Example 17

18. Classes Body part requiring rehabilitation FrequencyRelative FrequencyPercent Back120.440% Wrist20.077% Elbow10.033% Hip20.077% Shoulder40.1313% Knee50.1717% Hand20.077% Groin10.033% Neck10.033% n=30 1100% LEC3 Example 18

19. LEC3 * 19 Bar Chart

20. LEC3 * Percent 40% 7% 3% 7% 13% 17% 7% 3% Classes Back Wrist Elbow Hip Shoulder Knee Hand Groin Neck 7% 40% 3% 20 Pie Charts

21. cumulative % invested (line graph) % invested in each category (bar graph) LEC3 * 21 Pareto Diagram Example

22. LEC3 * Year Rate of Death 1985 3.56 19861.86 19873.65 19884.14 19894.82 19905.40 19914.21 19923.01 19932.99 19942.56 19952.83 19962.95 19972.29 19981.56 19992.21 20003.36 20012.85 20021.58 Line charts : show values of One variable vs. time is traditionally shown on the horizontal axis 22 Line Chart Example

23. Positive Correlation ● If the Y-coordinates are a increasing while the X- coordinates increasing, then it is POSITIVE CORRELATION. ● This means that both are going up, and they are related. LEC3 * Scatter Plot 23

24. Positive Correlation (Example) ● If you look at the age of a child and the child’s height, you will find that as the child gets older, the child gets taller. Because both are going up, it is positive correlation. Age12345678 Height “ 2531343640414755 LEC3 * Scatter Plot 24

25. Negative Correlation If the Y-coordinates are a decreasing while the X-coordinates increasing, then it is NEGATIVE CORRELATION ● This means that 1 is going up and 1 is going down, making a downhill graph. This means the two are related as opposites. LEC3 25 Scatter Plot

26. No Correlation ● If there seems to be no pattern, and the points looked scattered, then it is no correlation. ● This means the two are not related. LEC3 * Scatter Plot 26

27. 1. A positive correlation. As one quantity increases so does the other. 2. A negative correlation. As one quantity increases the other decreases. 3. No correlation. Both quantities vary with no clear relationship. Scatter graphs are used to show whether there is a relationship between two sets of data. The relationship between the data can be described as either: Shoe Size Annual Income Height Shoe Size Soup Sales Temperature Positive CorrelationNegative correlationNo correlation LEC3 * Scatter Graphs 27

28. LEC3 * Summary  Data in raw form are usually not easy to use for decision making -- Some type of organization is needed:  Table  Graph  Techniques reviewed in this chapter:  Frequency Distributions and Histograms  Frequency Polygon and Histogram/Frequency Polygon.  Bar Charts and Pie Charts  Stem and Leaf Diagrams  Line Charts and Scatter Diagrams 28

29. LEC3 *